Which of the following numbers is a multiple of 7? ${63,64,90,102,120}$
Explanation: The multiples of $7$ are $7$ $14$ $21$ $28$ ..... In general, any number that leaves no remainder when divided by $7$ is considered a multiple of $7$ We can start by dividing each of our answer choices by $7$ $63 \div 7 = 9$ $64 \div 7 = 9\text{ R }1$ $90 \div 7 = 12\text{ R }6$ $102 \div 7 = 14\text{ R }4$ $120 \div 7 = 17\text{ R }1$ The only answer choice that leaves no remainder after the division is $63$ $ 9$ $7$ $63$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $7$ are contained within the prime factors of $63$ $63 = 3\times3\times7 7 = 7$ Therefore the only multiple of $7$ out of our choices is $63$. We can say that $63$ is divisible by $7$.